机读格式显示(MARC)
- 000 02864cam a22003497i 4500
- 008 210608s2021 sz a b 001 0 eng d
- 020 __ |a 9783030806491 : |c CNY996.57
- 035 __ |a (OCoLC)1255466358
- 040 __ |a YDX |b eng |c YDX |e rda |d BXM |d OCLCO |d OCLCF |d OCLCO |d AS |d MATH
- 050 _4 |a QA689 |b .O48 2021
- 100 1_ |a Ohta, Shin-ichi, |e author.
- 245 10 |a Comparison Finsler geometry / |c Shin-ichi Ohta.
- 264 _1 |a Cham : |b Springer, |c [2021]
- 300 __ |a xxii, 316 pages : |b illustrations ; |c 24 cm
- 336 __ |a text |b txt |2 rdacontent
- 337 __ |a unmediated |b n |2 rdamedia
- 338 __ |a volume |b nc |2 rdacarrier
- 490 1_ |a Springer monographs in mathematics, |x 1439-7382.
- 504 __ |a Includes bibliographical references (pages 301-311) and index.
- 520 __ |a "This monograph presents recent developments in comparison geometry and geometric analysis on Finsler manifolds. Generalizing the weighted Ricci curvature into the Finsler setting, the author systematically derives the fundamental geometric and analytic inequalities in the Finsler context. Relying only upon knowledge of differentiable manifolds, this treatment offers an accessible entry point to Finsler geometry for readers new to the area. Divided into three parts, the book begins by establishing the fundamentals of Finsler geometry, including Jacobi fields and curvature tensors, variation formulas for arc length, and some classical comparison theorems. Part II goes on to introduce the weighted Ricci curvature, nonlinear Laplacian, and nonlinear heat flow on Finsler manifolds. These tools allow the derivation of the Bochner-Weitzenbock formula and the corresponding Bochner inequality, gradient estimates, Bakry-Ledoux's Gaussian isoperimetric inequality, and functional inequalities in the Finsler setting. Part III comprises advanced topics: a generalization of the classical Cheeger-Gromoll splitting theorem, the curvature-dimension condition, and the needle decomposition. Throughout, geometric descriptions illuminate the intuition behind the results, while exercises provide opportunities for active engagement. Comparison Finsler Geometry offers an ideal gateway to the study of Finsler manifolds for graduate students and researchers. Knowledge of differentiable manifold theory is assumed, along with the fundamentals of functional analysis. Familiarity with Riemannian geometry is not required, though readers with a background in the area will find their insights are readily transferrable"--Back cover.
- 650 _0 |a Finsler spaces.
- 650 _0 |a Manifolds (Mathematics)
- 650 _6 |a Espaces de Finsler.
- 650 _6 |a Variance (Mathematiques)
- 830 _0 |a Springer monographs in mathematics. |x 1439-7382.